Effective equivalence of the EinsteinCartan and Einstein theories of gravity
Abstract
It is proven that for any choice of minimally coupled sourcefield Lagrangian for the EinsteinCartanSciamaKibble theory of gravity, there exists a related minimally coupled sourcefield Lagrangian for the Einstein theory which produces the same field equations for the metric and source field. By using a standard firstorder form for source Lagrangians, the converse is also demonstrated. This establishes a onetoone correspondence between source Lagrangians for the two theories which clearly reveals their similarities and differences. Because of this 'equivalence,' one can view either theory, in terms of the other, as minimal coupling for a related Minkowski source Lagrangian or as nonminimal coupling for the same Minkowski source Lagrangian. Consequently the two theories are, in this sense, indistinguishable. Some other implications of this 'equivalence' are discussed.
 Publication:

Physical Review D
 Pub Date:
 October 1977
 DOI:
 10.1103/PhysRevD.16.2395
 Bibcode:
 1977PhRvD..16.2395N
 Keywords:

 Einstein Equations;
 Gravitation Theory;
 Kinematics;
 Spin Dynamics;
 Astronomical Models;
 Gravitational Fields;
 SpaceTime Functions;
 Transformations (Mathematics);
 Physics (General)